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The word MATH is repeatedly written producing the pattern MATHMATHMATH... If the pattern is continued, what letter will occur in the 1000th position?

 Jul 8, 2022
 #1
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See this pattern:

M - 1, 5, 9, 13, 17...

A - 2, 6, 10, 14, 18...

T: 3, 7, 11, 15, 19...

H: 4, 8, 12, 16, 20...

 

Do you think you can use this information to extrapolate the 1000th position? 

Edit: Think about 997, 998, 999, 1000. Where will these fall?

 Jul 8, 2022
edited by Katashio  Jul 8, 2022
 #2
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MATH has a "period of 4"

 

Therefore: 1000 mod 4 ==0, which means the last letter of MATH, or H

 Jul 8, 2022

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